Identification of Error Types in Preservice Teachers' Attempts to Create Fraction Story Problems for Specified Operations

The purpose of this research was to determine if recognizable error types exist in the work of preservice teachers required to create story problems for specific fraction operations. Students were given a particular single‐operation fraction expression and asked to do the calculation and then create a story problem that would require the use of both the expression and calculation to answer the story problem. Distinct error types, determined by mathematical and grammatical characteristics, were identified by the researchers. These error types were then used to analyze an additional set of work samples to determine frequency rates of error types. Future research will involve evaluating the efficacy of specific instructional methods with the goal of reducing the frequency of certain error types.     

The input impedance of the dielectric resonator antenna

Dielectric cylinders of very high permittivity have been used in the past as resonant cavities, but since the structure is not enclosed by metallic walls, electromagnetic fields do exist beyond the geometrical boundaries of the structure and part of the power is radiated. Through the proper choice of geometry and permittivity this radiation can become the dominant feature of the structure and become an efficient antenna for use at millimeter wave frequencies. Both experimental and theoretical investigations of a variety of these dielectric resonator antennas have been undertaken. In particular, the input impedance of a probe-fed cylindrical structure was examined in detail and a comparison of theoretical and experimental results was made.     

Solid phase approaches to N-heterocycles using a sulfur linker cleaved by SmI2

A sulfur HASC (alpha-hetero-atom substituted carbonyl) linker has been utilized in solid-phase approaches to oxindoles and tetrahydroquinolones. The route to oxindoles employs the first Pummerer cyclizations on solid phase, whereas the route to tetrahydroquinolones involves a microwave-assisted Heck reaction followed by a Michael cyclization. In both cases, the linker is cleaved in a traceless fashion by electron transfer from samarium(II) iodide. The routes illustrate the compatibility of the linker system with a number of reaction types and its utility for library synthesis.     

Relative stability of major types of beta-turns as a function of amino acid composition: a study based on Ab initio energetic and natural abundance data

Folding properties of small globular proteins are determined by their amino acid sequence (primary structure). This holds both for local (secondary structure) and for global conformational features of linear polypeptides and proteins composed from natural amino acid derivatives. It thus provides the rational basis of structure prediction algorithms. The shortest secondary structure element, the beta-turn, most typically adopts either a type I or a type II form, depending on the amino acid composition. Herein we investigate the sequence-dependent folding stability of both major types of beta-turns using simple dipeptide models (-Xxx-Yyy-). Gas-phase ab initio properties of 16 carefully selected and suitably protected dipeptide models (for example Val-Ser, Ala-Gly, Ser-Ser) were studied. For each backbone fold most probable side-chain conformers were considered. Fully optimized 321G RHF molecular structures were employed in medium level [B3LYP/6-311++G(d,p)//RHF/3-21G] energy calculations to estimate relative populations of the different backbone conformers. Our results show that the preference for beta-turn forms as calculated by quantum mechanics and observed in Xray determined proteins correlates significantly.     

Two-dimensional packing of short DNA with nonpairing overhangs in cationic liposome-DNA complexes: from Onsager nematics to columnar nematics with finite-length columns

We report the formation of liquid crystalline (LC) phases of short double-stranded DNA with nonpairing (nonsticky) overhangs, confined between two-dimensional (2D) lipid bilayers of cationic liposome-DNA complexes. In a landmark study (Science2007, 318, 1276), Nakata et al. reported on the discovery of strong end-to-end stacking interactions between short DNAs (sDNAs) with blunt ends, leading to the formation of 3D nematic (N) and columnar LC phases. Employing synchrotron small-angle X-ray scattering, we have studied the interplay between shape anisotropy-induced and DNA end-to-end interaction-induced N ordering for 11, 24, and 48 bp sDNA rods with single-stranded oligo-thymine (T) overhangs modulating the end-to-end interactions. For suppressed stacking interactions with 10-T overhangs, the volume fraction of sDNA at which the 2D isotropic (I)-to-N transition occurs for 24 and 48 bp sDNA rods depended on their length-to-width (L/D) shape anisotropy, qualitatively consistent with Onsager's theory for the entropic alignment of rigid rods. As the overhang length is reduced from 10 to 5 and 2 T for 24 and 48 bp sDNA, the N-to-I transition occurs at lower volume fractions, indicating the onset of some degree of end-to-end stacking interactions. The 11 bp sDNA rods with 5- and 10-T overhangs remain in the I phase, consistent with their small shape anisotropy (L/D ≈ 1.9) below the limit for Onsager LC ordering. Unexpectedly, in contrast to the behavior of 24 and 48 bp sDNA, the end-to-end interactions between 11 bp sDNA rods with 2-T overhangs set in dramatically, and a novel 2D columnar N phase (N(C)) with finite-length columns formed. The building blocks of this phase are comprised of 1D stacks of (on average) four 11 bp DNA-2T rods with an effective L(stacked)/D ≈ 8.2. Our findings have implications for the DNA-directed assembly of nanoparticles on 2D platforms via end-to-end interactions and in designing optimally packed LC phases of short anisotropic biomolecules (such as peptides and short-interfering RNAs) on nanoparticle membranes, which are used in gene silencing and chemical delivery.     

A density functional theory study of sulfur poisoning

Density functional theory calculations have been used to investigate the chemisorption of H, S, SH, and H(2)S as well as the hydrogenation reactions S+H and SH+H on a Rh surface with steps, Rh(211), aiming to explain sulfur poisoning effect. In the S hydrogenation from S to H(2)S, the transition state of the first step S+H-->SH is reached when the S moves to the step-bridge and H is on the off-top site. In the second step, SH+H-->H(2)S, the transition state is reached when SH moves to the top site and H is close to another top site nearby. Our results show that it is difficult to hydrogenate S and they poison defects such as steps. In order to address why S is poisoning, hydrogenation of C, N, and O on Rh(211) has also been calculated and has been found that the reverse and forward reactions possess similar barriers in contrast to the S hydrogenation. The physical origin of these differences has been analyzed and discussed.     

Data on subglottal pressure and SPL at varied vocalloudness and pitch in 8- to 11-year-old children

Phonation threshold pressure has been defined as the minimum subglottalpressure to generate phonation. Previous research has indicated that children may habitually employ higher subglottal pressures than adults. In the present investigation sound pressure level (SPL) and subglottal pressures at different pitch levels were measured at and above phonation threshold in nine children. Phonation threshold values were scattered in reasonable agreement with Titzes' prediction, although a discrepancy was noted regarding the frequency dependence in some voices. At normal conversational loudness and loudest level of phonation the children's PS values were between two to four and four to eight times the predicted threshold values, respectively. At normal conversational loudness and habitual pitch subglottal pressures were lower than those previously observed for children, but similar to those found for female adults. The SPL in softest and loudest phonation were somewhat lower as compared to previous phonetogram data for children and for female adults. At normal loudness and habitual pitch the SPL values were similar to those of female adults. For a doubling of P_s mean SPL increased by 10.5 dB on the average.     

A compact piecewise-linear voronoi diagram for convex sites in the plane

In the plane the post-office problem, which asks for the closest site to a query site, and retraction motion planning, which asks for a one-dimensional retract of the free space of a robot, are both classically solved by computing a Voronoi diagram. When the sites arek disjoint convex sets we give a compact representation of the Voronoi diagram, usingO (k) line segments, that is sufficient for logarithmic time post-office location queries and motion planning. If these sets are polygons withn total vertices given in standard representations, we compute this diagram optimally in Θ (k logn) deterministic time for the Euclidean metric and inO (k logn logm) deterministic time for the convex distance function defined by a convexm-gon. This work was supported by NSERC in the form of a Graduate Scholarship and two Research Grants.     

Degrees of stretched Kostka coefficients

Given a partition λ and a composition β, the stretched Kostka coefficient is the map n ↦ K _{n λ,n β} sending each positive integer n to the Kostka coefficient indexed by n λ and n β. Kirillov and Reshetikhin (J. Soviet Math. 41(2), 925–955, 1988) have shown that stretched Kostka coefficients are polynomial functions of n. King, Tollu, and Toumazet have conjectured that these polynomials always have nonnegative coefficients (CRM Proc. Lecture Notes 34, 99–112, 2004), and they have given a conjectural expression for their degrees (Séminaire Lotharingien de Combinatoire 54A, 2006). We prove the values conjectured by King, Tollu, and Toumazet for the degrees of stretched Kostka coefficients. Our proof depends upon the polyhedral geometry of Gelfand–Tsetlin polytopes and uses tilings of GT-patterns, a combinatorial structure introduced in De Loera and McAllister, (Discret. Comput. Geom. 32(4), 459–470, 2004). Research supported by NSF VIGRE Grant No. DMS-0135345 and by NWO Mathematics Cluster DIAMANT.